sainijasdeep27
10.06.2021 •
Mathematics
The number of texts per day by students in a class is normally distributed with a
mean of 130 texts and a standard deviation of 20 texts. Identify all true statements.
1. A little more than 2% of the students text
under 90 times per day.
2. About 50% of the students text more than 130 times per day.
3. About 15% of the students send over 190 texts per day.
4. About 68% of the students text between 100 and 130 times.
5. A student texting 130 times per day would have a z score of 1.
6. A student texting 160 times falls between 1 and 2 standard deviations from the mean.
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Ответ:
1, 2, 6
Step-by-step explanation:
The z score shows by how many standard deviations the raw score is above or below the mean. The z score is given by:
Given that mean (μ) = 130 texts, standard deviation (σ) = 20 texts
1) For x < 90:
From the normal distribution table, P(x < 90) = P(z < -2) = 0.0228 = 2.28%
Option 1 is correct
2) For x > 130:
From the normal distribution table, P(x > 130) = P(z > 0) = 1 - P(z < 0) = 1 - 0.5 = 50%
Option 2 is correct
3) For x > 190:
From the normal distribution table, P(x > 3) = P(z > 3) = 1 - P(z < 3) = 1 - 0.9987 = 0.0013 = 0.13%
Option 3 is incorrect
4) For x < 130:
For x > 100:
From the normal table, P(100 < x < 130) = P(-1.5 < z < 0) = P(z < 0) - P(z < 1.5) = 0.5 - 0.0668 = 0.9332 = 93.32%
Option 4 is incorrect
5) For x = 130:
Option 5 is incorrect
6) For x = 130:
Since 1.5 is between 1 and 2, option 6 is correct
Ответ:
Please, see the attached files.
Thanks.